QUICK QUESTION! (out of the curiousity) (1 Viewer)

[HeroicPandas]

Ok there is this question and I'm arguing with my friend:He says . I thought this is only true if the |z|=1... (ie. root of unity.)Also, the question stated that and

 

[seanieg89]

 

[HeroicPandas]

But 2 isn't complex

 

[D94]

But 2 isn't complex

2 is in the Complex field. 2 + 0i = 2.

 

[HeroicPandas]

Oh alright, thank you master sean and mmaster D94, BUT i seriously dont get it when they go and

 

[Carrotsticks]

For the record, all real numbers are complex numbers (since R is a subset of C).And indeed we have Z conjugate being equal to 1/Z when Z lies on the unit circle. Just consider the problem to be like a locus question.Z CAN be equal to 1.1 = 1 + 0iConjugate of 1 is 1 - 0i = 1Reciprocal of 1 is 1/1 = 1.I presume that they said z=/=0 because it is in the denominator. But Z cannot be zero anyway because for that condition to be satisfied, Z MUST lie on the unit circle.

 

[HeroicPandas]

Ok i have to say this, i forgot to say this was a LOCUS question lol, so my friend is wrong? and i am right yeh? about

 

[Carrotsticks]

Ok i have to say this, i forgot to say this was a LOCUS question lol, so my friend is wrong? and i am right yeh? about

The condition only holds if Z is on the unit circle, so you are indeed correct (assuming your friend made the claim for ALL complex numbers).

 

[HeroicPandas]

Yay! Thanks so much for helping me everyone!